General Mathematics - Assignment 1, Assignments of Mathematics

The document contains 2 assignment exercises for the subject General Mathematics (Domain and Functions). The assignments also include different answers (Domain, Zero of Function, Graph, Range, etc.) depending on what is needed.

Typology: Assignments

2020/2021

Available from 12/29/2022

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1.) f(x)=x+3
2x
Domain: 2x = 0 Range: y = x+3
2x
: 2x
2=0
2 : x = y+3
2y
: x = 0 : 3
2xโˆ’1
: x โˆˆ โ„|x โ‰  0 : 2๐‘ฅ โˆ’ 1 = 0
: 2๐‘ฅ = 1
: 2๐‘ฅ
2=1
2
: ๐‘ฅ = 1
2
: ๐‘ฆ โˆˆ โ„|๐‘ฆ โ‰  1
2
Zero of Function: ๐‘“(๐‘ฅ)=๐‘ฅ+3
2๐‘ฅ
: 0 = ๐‘ฅ+3
2๐‘ฅ
: 0(2๐‘ฅ)= ๐‘ฅ + 3
: 0 = ๐‘ฅ + 3
: ๐‘ฅ = โˆ’3
V. Asymptotes: 2๐‘ฅ = 0 H. Asymptotes: ๐‘ฆ = 1
2
: 2๐‘ฅ
2=0
2
: ๐‘ฅ = 0
Table of Values:
X
-3
-2
-1.5
-1
-0.6
y
0
-0.25
-0.5
-1
-2
pf3
pf4

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1.) f

x

x+ 3

2x

Domain: 2x = 0 Range: y =

x+ 3

2x

2x

2

0

2

: x =

y+ 3

2y

: x = 0 :

3

2xโˆ’ 1

: x โˆˆ โ„|x โ‰  0 : 2 ๐‘ฅ โˆ’ 1 = 0

2 ๐‘ฅ

2

1

2

1

2

1

2

Zero of Function: ๐‘“

๐‘ฅ+ 3

2 ๐‘ฅ

๐‘ฅ+ 3

2 ๐‘ฅ

V. Asymptotes: 2 ๐‘ฅ = 0 H. Asymptotes: ๐‘ฆ =

1

2

2 ๐‘ฅ

2

0

2

Table of Values:

X - 3 - 2 - 1.5 - 1 - 0. 6

y 0 - 0.25 - 0. 5 - 1 - 2

Graph:

Table of Values:

X - 2 1 - 0.236 0. 172 0.

y - 1. 667 0 2 4 5

Graph: